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The cells of a 11x11 chess board are colored in 3 colors

Source: Romanian IMO Team Selection Test TST 1988, problem 5

October 1, 2005
geometryrectanglecombinatorics proposedcombinatorics

Problem Statement

The cells of a 11×1111\times 11 chess-board are colored in 3 colors. Prove that there exists on the board a m×nm\times n rectangle such that the four cells interior to the rectangle and containing the four vertices of the rectangle have the same color. Ioan Tomescu
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